An inverse problem for Dirac systems on p-star-shaped graphs

Abstract

In this paper, we study direct and inverse problems for Dirac systems with complex-valued potentials on p-star-shaped graphs. More precisely, we firstly obtain sharp 2-term asymptotics of the corresponding eigenvalues. We then formulate and address a Horváth-type theorem, specifically, if the potentials on $p-1$ edges of the p-star-shaped graph are predetermined, we demonstrate that the remaining potential on $[0,\pi ]$ can be uniquely determined by part of its eigenvalues and the given remaining potential on $[a,\pi ]$, $0<a\le \pi$, under certain conditions.